.\" Copyright (c) 1990, 1991, 1993
.\"	The Regents of the University of California.  All rights reserved.
.\"
.\" This code is derived from software contributed to Berkeley by
.\" the American National Standards Committee X3, on Information
.\" Processing Systems.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\"    notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\"    notice, this list of conditions and the following disclaimer in the
.\"    documentation and/or other materials provided with the distribution.
.\" 4. Neither the name of the University nor the names of its contributors
.\"    may be used to endorse or promote products derived from this software
.\"    without specific prior written permission.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\"     @(#)qsort.3	8.1 (Berkeley) 6/4/93
.\" $FreeBSD$
.\"
.Dd September 30, 2003
.Dt HEAPSORT 3bsd
.Os
.Sh NAME
.Nm heapsort , mergesort
.Nd sort functions
.Sh LIBRARY
.ds str-Lb-libbsd Utility functions from BSD systems (libbsd, \-lbsd)
.Lb libbsd
.Sh SYNOPSIS
.In stdlib.h
(See
.Xr libbsd 7
for include usage.)
.Ft int
.Fo heapsort
.Fa "void *base"
.Fa "size_t nmemb"
.Fa "size_t size"
.Fa "int \*[lp]*compar\*[rp]\*[lp]const void *, const void *\*[rp]"
.Fc
.Ft int
.Fo mergesort
.Fa "void *base"
.Fa "size_t nmemb"
.Fa "size_t size"
.Fa "int \*[lp]*compar\*[rp]\*[lp]const void *, const void *\*[rp]"
.Fc
.Sh DESCRIPTION
The
.Fn heapsort
function is a modified selection sort.
The
.Fn mergesort
function is a modified merge sort with exponential search
intended for sorting data with pre-existing order.
.Pp
The
.Fn heapsort
function sorts an array of
.Fa nmemb
objects, the initial member of which is pointed to by
.Fa base .
The size of each object is specified by
.Fa size .
The
.Fn mergesort
function
behaves similarly, but
.Em requires
that
.Fa size
be greater than
.Dq "sizeof(void *) / 2" .
.Pp
The contents of the array
.Fa base
are sorted in ascending order according to
a comparison function pointed to by
.Fa compar ,
which requires two arguments pointing to the objects being
compared.
.Pp
The comparison function must return an integer less than, equal to, or
greater than zero if the first argument is considered to be respectively
less than, equal to, or greater than the second.
.Pp
The algorithm implemented by
.Fn heapsort
is
.Em not
stable, that is, if two members compare as equal, their order in
the sorted array is undefined.
The
.Fn mergesort
algorithm is stable.
.Pp
The
.Fn heapsort
function is an implementation of
.An "J.W.J. William" Ns 's
.Dq heapsort
algorithm,
a variant of selection sorting; in particular, see
.An "D.E. Knuth" Ns 's
.%T "Algorithm H" .
.Sy Heapsort
takes O N lg N worst-case time.
Its
.Em only
advantage over
.Fn qsort
is that it uses almost no additional memory; while
.Fn qsort
does not allocate memory, it is implemented using recursion.
.Pp
The function
.Fn mergesort
requires additional memory of size
.Fa nmemb *
.Fa size
bytes; it should be used only when space is not at a premium.
The
.Fn mergesort
function
is optimized for data with pre-existing order; its worst case
time is O N lg N; its best case is O N.
.Pp
Normally,
.Fn qsort
is faster than
.Fn mergesort
is faster than
.Fn heapsort .
Memory availability and pre-existing order in the data can make this
untrue.
.Sh RETURN VALUES
.Rv -std heapsort mergesort
.Sh ERRORS
The
.Fn heapsort
and
.Fn mergesort
functions succeed unless:
.Bl -tag -width Er
.It Bq Er EINVAL
The
.Fa size
argument is zero, or,
the
.Fa size
argument to
.Fn mergesort
is less than
.Dq "sizeof(void *) / 2" .
.It Bq Er ENOMEM
The
.Fn heapsort
or
.Fn mergesort
functions
were unable to allocate memory.
.El
.Sh SEE ALSO
.Xr sort 1 ,
.Xr radixsort 3bsd
.Rs
.%A Williams, J.W.J
.%D 1964
.%T "Heapsort"
.%J "Communications of the ACM"
.%V 7:1
.%P pp. 347-348
.Re
.Rs
.%A Knuth, D.E.
.%D 1968
.%B "The Art of Computer Programming"
.%V Vol. 3
.%T "Sorting and Searching"
.%P pp. 114-123, 145-149
.Re
.Rs
.%A McIlroy, P.M.
.%T "Optimistic Sorting and Information Theoretic Complexity"
.%J "Fourth Annual ACM-SIAM Symposium on Discrete Algorithms"
.%V January 1992
.Re
.Rs
.%A Bentley, J.L.
.%A McIlroy, M.D.
.%T "Engineering a Sort Function"
.%J "Software--Practice and Experience"
.%V Vol. 23(11)
.%P pp. 1249-1265
.%D November\ 1993
.Re
